Can you Sudoku?

My apologies if you were disturbed by a howl of anguish followed by the sound of tearing newspaper just before lunchtime yesterday: I had just experienced my first "Sudoku moment".

Twenty minutes of intense concentration, logical deduction and scribbling had been rendered worthless by the infuriating discovery that the number 4 appeared twice in the same line of squares.

That is very bad when playing Sudoku. In fact, that is exactly what one is trying to avoid. It means that you have to begin unpicking much of what you have done; in my case it meant starting all over again.

Thanks to the Daily Mail - where the puzzles were first introduced to this country and appear each day as the 'Codenumber' game - such agonies are repeated tens of thousands of times a day across Britain as the craze for Sudoku gathers pace.

It has been described as the Rubik's Cube of the 21st century. It is simple, yet fiendish, accessible to all in its various levels of difficulty and, once played, utterly addictive. And yet Sudoku was introduced to this country by the Mail only last November.

Since then, it is fair to say, the game has become a phenomenon among those who like to while away their tea break or commute to work by exercising their brains with a puzzle (some say it may even stave off the deterioration of mental capability caused by ageing).

A Sudoku book currently stands at No 34 in the national bestsellers' list, the internet is awash with sites devoted to the game and soon we will be able to download versions of it onto our mobile phones.

So much for the hype. For the benefit of those still uninitiated - and I was converted only yesterday - one should first answer the obvious question: what exactly is Sudoku?

Japanese game

If the name sounds Japanese, that's because it is: Sudoku came to this country from the puzzle-crazy Land of the Rising Sun.

Translated into English, 'Sudoku' - or 'Su doku' as some call it - means something like "Single Number".

One could describe it, also loosely, as a crossword puzzle using numbers instead of words.

Of course, it does not demand the same linguistic skills, lateral thought or general knowledge as a crossword. But nor does a Sudoku player have to possess any mathematical skills.

There is no adding up, subtraction, multiplication or division in Sudoku. You do not even need to know that two plus two equals four. But, boy, can it make your brain ache, your pulse race and knuckles whiten as you grip your pen in exasperation or, finally, ecstasy!

The classic Sudoku game involves a grid of 81 squares. The grid is divided into nine blocks, each containing nine squares.

The object of the game is this: Each of the nine blocks has to contain all the numbers 1-9 within its squares. Sound easy? It is& and yet it isn't.

The difficulty lies in that each vertical nine-square column, or horizontal nine-square line across, within the larger square, must also contain the numbers 1-9, without repetition or omission.

The creator of a particular puzzle will have filled in several of the squares to set you on your way. The rest is up to your ability to employ simple logic. Addicts claim a factory hand can be as adept at Sudoku as a university professor.

Swiss origins

Although Sudoku is a Japanese import, its roots lie in the work of an 18th-century Swiss genius. Leonhard Euler, who was born in Basle in 1707 and has been described as one of the greatest mathematicians of all time.

Plagued by eyesight problems that eventually led to blindness, Euler nevertheless produced formulas in every branch of mathematics, wrote 886 books and papers and also found the time and energy to father 13 children.

But the idea that is saluted every day, albeit unknowingly, by fans of Sudoku is Euler's "Latin Squares", which he introduced in 1783 as a "nouveau espece de carres magiques", which translates as "a new kind of magic squares".

This was a grid of equal dimensions in which every number or symbol occurs once in each row or column. It differs from the Sudoku grid only in that the latter is subdivided into blocks of nine.

Sudoku's modern worldwide vogue can be traced back to the early 1980s, when it appeared in an American puzzle magazine under the name of the "Number Place" game.

This was noted by the Japanese puzzle magazine publishers Nikoli. Its attraction was that it transcended language barriers and, in any case, Japanese does not lend itself to crosswords because of the nature of its alphabet. Nikoli copied the idea and introduced it to its readers in 1984.

It was such a hit that there are now five Sudoku magazines published in Japan each month, with a total circulation of 660,000.

The Sudoku name is registered as a trademark in Japan, so rivals run it under the original US name of Number Place.

World championships

Thanks to its reliance on numbers rather than words, Sudoku has been included in several World Puzzle Championships. The phenomenon came to the attention of the Mail last year and since then readers have been given a Sudoku puzzle to solve each weekday. Purists say there should be only one solution to any Sudoku puzzle, although that is not always the case.

It has been said that in a classic 81-square Sudoku grid, the fewest number of squares that can be filled in by the creator for the reader to have any chance of finishing the puzzle is 19.

But no one seems yet to have calculated how many Sudoku variations there could be. Some websites claim the possibilities are infinite, though mathematically, that surely cannot be so.

One new fan, retired academic Dr Maya Slater, plays Sudoku each day after lunch over a cup of coffee and piece of chocolate, with her retired hospital consultant husband, Nicky.

She says: "The joy is the way it all falls into place suddenly. You have to do a certain amount of reasoning and so you have to exercise your little grey cells. We are told we should keep our brains in trim as we get older and this is a very nice way of doing it.

"The fiendish ones are more fun," she adds. "I would recommend making a copy of the grid next to the newspaper as, if mistakes are made, the grid can often disappear under a mass of corrections."

Peter Sterling supplies the Sudoku puzzle to the Daily Mail. Describing the early days of compiling them, he said: "We started off very much on a trial and error basis. But after a while we found there are certain number of patterns that crop up time and again.

"After we have filled in the grid, the second stage is to select which numbers we should give to the reader to start them off. Of course, that is what largely makes up the difficulty of the puzzle.

"For the Daily Mail, we normally supply 32 of the 81 numbers. This tends to make for a puzzle of medium difficulty. It's a tricky thing to get the balance right because you don't want to lose too many players by making it nigh on impossible."

Peter claims that while other Sudoku compilers use computer software to create their puzzles, his are the work of "human hands", although they are then checked for validity by a software programme.

Of course, computers can also be used to cheat at Sudoku. The Mail is aware of at least three computer programmes designed to solve the puzzle without having to give it any thought.